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Glue Spin $S_G$ in The Longitudinally Polarized Nucleon

We present a lattice QCD calculation of the glue spin $S_G$ in the nucleon for the first time. It was recently shown that the first moment of the glue helicity distribution could be obtained through the cross-product of the the electric field $\vec{E}$ and the physical gauge field $\vec{A}_{phys}$ with the non-Abelian Coulomb gauge condition, i.e. $\int d^3 x\, \,\vec{E}(x) \times \vec{A}_{phys}(x)$ in the infinite momentum frame. We use the gauge field tensor from the overlap Dirac operator to check the frame dependence and calculate glue spin with several momenta. The calculation is carried out with valence overlap fermion on 2+1 flavor DWF gauge configurations on the $24^3 \times 64$ lattice with $a^{-1}=1.77$ GeV with the light sea quark mass corresponding to a pion mass of 330 MeV.